STOCHASTIC COMPARISONS and AGING PROPERTIES of an EXTENDED GAMMA PROCESS Zeina Al Masry, Sophie Mercier, Ghislain Verdier
STOCHASTIC COMPARISONS AND AGING PROPERTIES OF AN EXTENDED GAMMA PROCESS Zeina Al Masry, Sophie Mercier, Ghislain Verdier To cite this version: Zeina Al Masry, Sophie Mercier, Ghislain Verdier. STOCHASTIC COMPARISONS AND AGING PROPERTIES OF AN EXTENDED GAMMA PROCESS. Journal of Applied Probability, Cambridge University press, 2021, 58 (1), pp.140-163. 10.1017/jpr.2020.74. hal-02894591 HAL Id: hal-02894591 https://hal.archives-ouvertes.fr/hal-02894591 Submitted on 9 Jul 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Applied Probability Trust (4 July 2020) STOCHASTIC COMPARISONS AND AGING PROPERTIES OF AN EXTENDED GAMMA PROCESS ZEINA AL MASRY,∗ FEMTO-ST, Univ. Bourgogne Franche-Comt´e,CNRS, ENSMM SOPHIE MERCIER & GHISLAIN VERDIER,∗∗ Universite de Pau et des Pays de l'Adour, E2S UPPA, CNRS, LMAP, Pau, France Abstract Extended gamma processes have been seen to be a flexible extension of standard gamma processes in the recent reliability literature, for cumulative deterioration modeling purpose. The probabilistic properties of the standard gamma process have been well explored since the 1970's, whereas those of its extension remain largely unexplored. In particular, stochastic comparisons between degradation levels modeled by standard gamma processes and aging properties for the corresponding level-crossing times are nowadays well understood.
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